Lemma 2.2 (cf. [1]}) For any l.s.c. function \(\psi :X\rightarrow [0,\infty ]\) , any measure \(\mu \in \mathfrak {M}^+\) , and any \(\mu \) -measurable set \(A\subset X\) ,
\(\int \psi \,d\mu |_A=\lim _{K\uparrow A}\,\int \psi \,d\mu |_K.\) 

